Googology Wiki:About
Googology Wiki is an online community and wiki encyclopedia devoted to googology, the study of large numbers and their nomenclature. It boasts articles on numbers big and small—some everyday, and some far beyond human comprehension. This wiki was created four years ago in December 2008, with the intent of gathering the sporadic large number community into a single place. This page is a general FAQ about googology and the wiki. Googology What is googology? Googology is an obscure field of mathematics dedicated to studying and naming big numbers. It is a strange cross between a mathematical field, an art form, and an odd hobby. See our article on the subject for a description and a short essay on the history of large numbers. Large numbers have been part of human society ever since we could imagine them, but the term "googology" and the unification of large number studies are much newer. A Google search for the word returns only about 5,000 results as of January 2013. Googology has nothing to do with the search engine. The study of Google is called "googlology." (Google is, in fact, a misspelling of "googol" that stuck.) Isn't this a waste of time? Not completely. Large numbers can arise out of much more practical mathematical studies. Some examples are Graham's number (from Ramsey theory), the fast-growing hierarchy (from set theory), and n(4)/TREE(3)/SCG(13) (from combinatorics). Other large numbers were invented purely for entertainment, such as zootzootplex and Clarkkkkson. Overall, googology is recreational mathematics, although sometimes it flirts with more serious topics. Why the @&#$ are you doing this? Okay, honestly? We do googology because it's fun. It's immensely entertaining to toy with concepts that we know we'll never be able to comprehend. Googology is a bit like theology, except you make up your own gods and you can usually prove they exist. As with many nerdy subcultures, people get mad at us and do the whole "you guys could be curing cancer"/"nobody cares about math" schtick. If you're one of those people, buzz off and go play your World of Warcraft or something. We don't need your kind here. Still with us? Good. Where can I learn more about googology? We're flattered by your interest! Here are two newbie-friendly sites: *Sbiis Saibian's in-progress Web book is an excellent introduction to the field, meant to appeal to both novices and hardcore googolsmiths. Sbiis gives you a tour of the history of this weird little field, and gives you an inside view of the googologist's mind as he walks you through the creation of a new function, hyper-E notation. And yes, this wiki is weakly affiliated with the book. *Robert Munafo has created an extensive tour of numbers small to big, reaching all the way into Cantor's infinities. For more technical sites, see our links page. Can't you can just add 1? Googologists are concerned with large numbers, but more specifically interesting large numbers. 54778027816477 is not as interesting as 7625597484987 — the former is mostly meaningless but the latter is actually \(3^{3^3}\). Besides, adding 1 is a really slow way of reaching for larger numbers. You can multiply or exponentiate. Or better, tetrate! I know the biggest number! Infinity! Okay, so what's infinity? Infinity is merely a symbol and not a number. Set theory deals with special numbers called ordinals that deal with well-defined infinities. Cantor's \(\omega\) is, roughly, the smallest number greater than all the positive integers. However, it's not the only infinity — it can be manipulated as in \(\omega + 1\) and \(\omega^2\). In fact, there's a vast hierarchy of wacky ordinal infinities such as \(\varepsilon_0\) and \(\Gamma_0\). Perhaps surprisingly, these infinities are useful in the study of large finite numbers! See the fast-growing hierarchy. What are googol and googolplex? How big are they? Googol is = 10 × 10 × ... × 10 × 10 (100 times) = 1 followed by 100 zeroes. For comparison, the number of subatomic particles in the observable universe is estimated to about . Googol is larger than million, billion, trillion, ... The 33rd member of this series, tretrigintillion = , is the first one to surpass googol. In exact terms, it is 10 duotrigintillion. It is possible and not too difficult to write out a googol. The author managed to do it in 45 seconds. Googolplex is }} = = 10 × 10 × ... × 10 × 10 (googol times) = 1 followed by googol zeroes. It is not googol + googol or googol × googol or , the first ones being too small and the last one being too big ( }}). I will say this once more — googolplex is 10 to the power of googol. Nothing else! Writing out a googolplex in any font size would take up more space than the observable universe can hold. Is googolplex the largest number? Nope! This is a common misconception (and a bizarrely illogical one). Googolplex + 1 is well-defined, and that's enough to show that googolplex is not the largest number. Googologists don't like to "just add 1 and be done with it," though. Okay then, is googolplex the largest named number? Nope! There's googolplexian (googolplexplex), giggol, gaggol, grangol, tritri, gongulus, bongulus... and a lot more! The largest named number as of March 2013 is Rayo's number, which is so large that its value can't be found even with an infinite computer! Before you go out and define , do remember that googologists are interested in finding elegant ways to reach new large numbers, not taking existing numbers and adding random junk to them. I heard that googol was coined by a kid. Is this true? The whole story is a classic legend of mathematical folklore. Googol was coined in 1938 by a 9-year-old Milton Sirotta when his uncle Edward Kasner, a mathematician and writer, asked for a name for the number. Milton then defined "googolplex" as "1, followed by writing zeroes until you get tired." Kasner, unimpressed with this subjective definition, redefined it to }}. The two numbers first appeared in Kasner's book, Mathematics and the Imagination. Googolplexplex came much later, and was probably invented independently by several people. What's BEAF? BEAF stands for Bowers Exploding Array Function. Read the article. What's the fast-growing hierarchy? Read the article. If it's too technical, there's an incomplete introduction. Googology Wiki I made up some numbers. Can I post them? This wiki is not a place to publicize a bunch of things you made up. Rather, it acts as a general encyclopedia of large numbers collected from various sources. So, if you've made up numbers, you should do two things: # Ensure that the numbers are published somewhere already. Googology Wiki requires citations for all encyclopedia contributions. #: Due to the small size of the topic, we aren't as strict as Wikipedia is. We're okay with personal websites and self-published sources. # Make sure the community is ok with where your numbers are coming from. This is just courtesy, and it may not be necessary. Note that even if you don't publish your numbers, it's still possible to get the word out to the googology community! See below. What are blogs? How do I make them? Googology Wiki is both an encyclopedia and a discussion forum for large number studies. Blogs are a way to get your ideas out to the community. You need to have a registered Wikia account to make a blog. Once you have an account, click on your username in the upper right (or click ), click on the "Blog" tab, and press "Create Blog Post." How do I create fancy-looking equations? Googology Wiki uses LaTeX (tutorial), and more specifically MathJax. Use \(x + 1 = 2\) for inline equations and \+ 1 = 2\ for separate ones. The built-in MediaWiki math system also works, but we don't use it anymore.